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Notes -
Yes, it is.
"P(M) = P(M|E)P(E) + P(M|¬E)P(¬E)" is a tautology, true for for any valid probabilities and conditional probabilities P with events E and M. Likewise for the identity "P(¬E)=1-P(E)". Combining the two gives
P(M) = P(M|E)P(E) + P(M|¬E)(1-P(E))
To say that "E is evidence for M" is to assert "P(M|E) > P(M)", and if we use that (along with "P(E)>0") we can derive the inequality
P(M) > P(M)P(E) + P(M|¬E)(1-P(E))
Subtract "P(M)P(E)" from both sides, then divide by 1-P(E) (using "P(E)<1"), and we get
P(M) > P(M|¬E)
which is to say that "absence of E is evidence against M".
The magnitude of the evidence depends greatly on the specifics, and can be negligible, but it's never zero.
Perhaps it is more accurate to my position to say that absence of admitted evidence is not evidence of absence. Because there's "evidence" for practically every insane position in the world. This leads people to want to exclude evidence on the basis of it not being high-quality enough. Now, a certain amount of this is admirable and good, because it keeps you sane!
But some people, even subconsciously, use this to simply exclude all the evidence they like, and then having excluded all the evidence they dislike, declare there to be no evidence to the contrary position.
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